-LRB- CNN -RRB- -- Manchester City crashed out of European competition following a 1-0 defeat at Borussia Dortmund .

Julian Schieber scored the only goal of the game to claim victory for the Germans and kill off any hopes City had of reaching the Europa League .

City has endured a dismal Champions League campaign and knew its hopes of reaching the last-16 had already faded before the trip to Dortmund .

But it had hoped to at least pick up the consolation of making it through to the Europa League , especially with Ajax facing Real Madrid at the Bernabeu .

English Premier League 's hidden costs revealed

But that dream was left shattered as the English Premier League champions were given a reality check .

Boss Roberto Mancini will now look ahead to Sunday 's Manchester derby after his team became the first from England to not win a single group game in the competition .

`` We lost our qualification tonight , '' he told reporters . `` We lost it before tonight , we tried -LRB- to qualify -RRB- but we 're missing more players . We had the chance to score but if in these moments you do n't score it 's difficult to win .

`` We are not in the Europa League , and for this we should be disappointed . ''

Elsewhere in Group D , Kaka scored the 28th Champions League goal of his career to become the all-time leading Brazilian goalscorer in the competition .

The Real Madrid star was on target during his side 's 4-1 win over Ajax with Cristiano Ronaldo and a brace from Jose Callejon completing the rout .

Kaka 's strike takes him past former Barcelona star Rivaldo , who had led the way with 27 goals to his name .

Messi and Ronaldo battle for Ballon d'Or

Ronaldo 's effort was his 61st goal of 2012 , one more than last year , and his seventh against Ajax in the Champions League .

The win means Real qualify in second place behind Borussia Dortmund .

In Group A , Paris Saint-Germain claimed a 2-1 victory and top spot against Porto with both teams already having qualified for the next stage .

Thiago Silva and Ezequiel Lavezzi were on target for the home side with Jackson Martinez netting for Porto , which finishes second in the group .

Dynamo Kiev was forced to play through a snow storm during its 1-1 draw at Dinamo Zagreb .

Both teams were led off the field with just 11 minutes on the clock as a blizzard forced the game to be halted .

After a 17 minute delay , it was Kiev which looked like emerging victorious thanks to Andriy Yarmolenko 's strike on the stroke of halftime .

But a 90th minute penalty by Ivan Krstanović , Dinamo 's first goal of the competition , rescued a point for his side .

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Schalke topped Group B following a hard-fought 1-1 draw at Montpellier .

The German side took a 56th minute lead through Benedikt Höwedes only for Emanuel Herrera to grab an equalizer .

Olympiakos will play in the Europa League following its 2-1 win against an Arsenal side , which had already qualified for the last-16 .

The visitors had taken the lead through Tomas Rosicky but goals from Giannis Maniatis and Kostas Mitroglou gave the Greek side victory .

Mexes wonder goal lifts Milan into knockout stages

In Group C , Zenit St.Petersburg pulled off a shock 1-0 win at AC Milan .

Captain Danny scored the only goal of the game after 35 minutes to ensure the Russian side 's place in the Europa League .

Milan finish second in the group , four points behind winners Malaga .

The La Liga club , which was held 2-2 by Anderlecht , became the first side from Spain to start a Champions League game with just one Spanish player .

Duda scored both goals for Malaga with Anderlecht 's strikes coming from Milan Jovanovic and Dieumerci Mbokani .

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Manchester City crashes out of Europe following 1-0 defeat in Dortmund

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Kaka becomes the all-time leading Brazilian goalscorer in the Champions League

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Zenit records shock 1-0 win at AC Milan to secure Europa League berth

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Olympiakos defeats Arsenal 2-1 to qualify for Europa League